In most mobile communication systems of today, there are specific requirements regarding cell search and synchronization of a radio base station and a mobile terminal in order to secure a correct data transmission. One example of such a system is the Universal Terrestrial Radio Access Network (UTRAN). There are also a number of other such mobile communication systems that have corresponding needs regarding cell search and synchronization.
In such mobile communication systems, synchronization is often performed both in uplink and downlink. In one step of the synchronization, e.g., downlink synchronization, the mobile terminal synchronizes to the carrier frequency and the frame timing of the radio base station. This synchronization, however, is not sufficient to ensure that the radio base station can properly receive the signals from the mobile terminals, since the mobile terminals may be located at various distances relative to the radio base station.
Consequently, further synchronization, e.g., uplink synchronization, is needed since the distance between a radio base station and a mobile terminal, and hence the round trip time, is in general unknown.
For uplink synchronization of the mobile terminals, a random access channel (RACH) can be used. RACH is in some systems contention-based, which means any mobile terminal within the cell may transmit on the resource allocated to RACH. Consequently, several mobile terminals may attempt to transmit synchronization signals simultaneously. In order to reduce the risk that the radio base station fails to distinguish signals from different mobile terminals, a set of random access preamble sequences is provided, a set being two or more preamble sequences, wherein each mobile terminal randomly selects one such random access preamble sequence. The random access preamble sequences selected by each mobile terminal can then be uniquely distinguished by the radio base station.
In a cell search situation, it could also be possible for a mobile terminal to choose one of a number of different preambles to send to a radio base station. The choice of one of these preambles, made by the mobile terminal, could in this case then also convey some information to the radio base station, e.g. telling the radio base station which services the mobile terminal requests.
Successful detection of the random access preamble sequence is necessary for the mobile terminal to access the network. It is therefore important that the transmitted random access preamble sequence requires a low power amplifier back-off to allow for high average transmit power and hence a good coverage.
The random access preamble sequences in the uplink should preferably have the following properties:                good autocorrelation properties to allow for an accurate timing estimation,        good cross-correlation properties to allow for an accurate timing estimation of different simultaneous and partially synchronized (i.e. downlink synchronized) preamble sequences, wherein the phase difference is limited by the maximum round-trip time in the cell, and        zero cross-correlation for synchronous and simultaneous preamble sequences.        
These properties are satisfied by the use of Zero-Correlation Zone (ZCZ) sequences. ZCZ sequences should thus preferably be used for the preamble sequences used in cell search and synchronization. ZCZ sequences can be derived from Generalized Chirp-Like (GCL) sequences, which are described in the following.
Generalized chirp-like (GCL) sequences belong to the family of Constant Amplitude Zero AutoCorrelation (CAZAC) sequences. The CAZAC sequences have ideal periodic autocorrelation and close to ideal aperiodic autocorrelation. Zero periodic autocorrelation in at least a zone around zero delay is an important property of a transmitted sequence to enable an accurate time-of-arrival estimation. Furthermore, the CAZAC sequences have a constant amplitude. A band-limited signal obtained by pulse-shaping of a CAZAC sequence will have small power variations, thus allowing for the use of low-cost power amplifiers and high efficiency.
GCL sequences are modulated Zadoff-Chu sequences, see further reference B. M. Popovic, “Generalized Chirp-Like Polyphase Sequences with Optimum Correlation Properties,” IEEE Trans. on Information Theory, Vol. 38, no. 4, pp 1406-1409, July 1992 (hereinafter “Popovic I”).
A GCL sequence {c(k)} is defined asc(k)=a(k)b(k mod m), k=0, 1, . . . , N−1,  (1)
where N=sm2, s and m are positive integers, {b(k)} is any sequence of m complex numbers of unit magnitude, and {a(k)} is the Zadoff-Chu sequence
                              a          ⁡                      (            k            )                          =                  {                                                                                                                                                                  W                          N                                                      k                                                                                          2                                /                                2                                                            +                              qk                                                                                                      ,                                                                                                            N                        ⁢                                                                                                  ⁢                        even                                                                                                                                                                          W                          N                                                                                                                    k                                ⁡                                                                  (                                                                      k                                    +                                    1                                                                    )                                                                                            /                              2                                                        +                            qk                                                                          ,                                                                                                                                      N                          ⁢                                                                                                          ⁢                          odd                                                ,                                                                                            ⁢                                                                  ⁢                k                            =              0                        ,            1            ,            …            ⁢                                                  ,                          N              -              1                        ,                          q              ⁢                                                          ⁢              is              ⁢                                                          ⁢              an              ⁢                                                          ⁢              integer                        ,                                              (        2        )            
where WN=exp(−j2πr/N) and r is relatively prime to N. Wnp is a shorthand notation for exp(−j2πrp/n).
If two GCL sequences cx(k) and cy(k) are defined by using the same Zadoff-Chu sequence {a(k)} but different arbitrary orthogonal modulation sequences {bx(k)} and {by(k)}, they are so-called zero-correlation zone (ZCZ) sequences, i.e. the periodic cross-correlations are zero for all shifts p such that 0≦p|≦T, where T=sm−1 is the length of the zero correlation zone. The aperiodic cross-correlations are in general low for shifts within the zero-correlation zone. The low cross-correlation property allows for detection of several quasi-simultaneous transmissions of different GCL sequences based on the same Zadoff-Chu sequence, even when the received signal powers are very different.
From the autocorrelation and cross-correlation properties as well as the limited power variations, a set of orthogonal GCL sequences using the same Zadoff-Chu sequence is therefore useful for non-synchronized random access preambles.
A detector, in, for instance, a radio base station transceiver, for non-synchronized random access preambles based on such a set of GCL sequences needs to correlate the received signal with all sequences in the set of GCL sequences for a range of delays. Such correlations are computationally complex.